The phantom of transparency

Jean-Yves Girard

Description

Niveau: Supérieur, Doctorat, Bac+8
The phantom of transparency Jean-Yves Girard Institut de Mathématiques de Luminy, UMR 6206 – CNRS 163, Avenue de Luminy, Case 930, F-13288 Marseille Cedex 09 February 8, 2008 Per te, Peppe. I will discuss the status of the implicit and the explicit in science, mostly in logic1. I will especially denunciate, expose a deep and pregnant unsaid of scientific activity : the subliminal idea that, beyond immediate perception, could exist a world, a layer of reading, completely intelligible, i.e., explicit and immediate. What I will call the fantasy (or phantom, as a matter of joke) of transparency. Transparency has little to do with poetical ideas (the key of dreams, etc.). It is indeed a unidimensional underside of the universe, not always monstrous, but anyway grotesque. Think of this Axis of Evil supposedly responsible of all the misery of the world, or of these unbelievable minority studies which expose the carefully concealed truths : for feminine studies Shakespeare was a woman, for african studies he was an Arab, the Cheikh Zubayr ! Nevertheless, everything starts from a correct premise, to go beyond mere apparences ; but, to do so, one imagines an A other side of the mirror B whose delimitations are neat, precise, without the slightest ambiguity : the world is seen as a rebus of which it suffices to find the key.

• expression originally refers


• transparency


• epistemic logic


• into intellectual


• explicit thus


• who stays silent


• transparency takes


• logic never


• yezhov's ante litteram

Sujets

• Zubayr
• Girard
• Léonid Brejnev
• Guantánamo
• Sarkozy (surname)
• Transparency
• Epistemic modal logic

Informations

• Publié par: mijec
• Nombre de lectures: 25
• Langue: English

Extrait

The phantom of transparency
Jean-Yves Girard
Institut de Mathématiques de Luminy, UMR 6206 – CNRS
163, Avenue de Luminy, Case 930, F-13288 Marseille Cedex 09
[e-mail]
February 8, 2008
Per te, Peppe.
I will discuss the status of the implicit and the explicit in science, mostly
1in logic . I will especially denunciate, expose a deep and pregnant unsaid of
scientific activity : the subliminal idea that, beyond immediate perception,
could exist a world, a layer of reading, completely intelligible, i.e., explicit
and immediate. What I will call the fantasy (or phantom, as a matter of
joke) of transparency.
Transparency has little to do with poetical ideas (the key of dreams,
etc.). It is indeed a unidimensional underside of the universe, not always
monstrous, but anyway grotesque. Think of this Axis of Evil supposedly
responsible of all the misery of the world, or of these unbelievable minority
studies which expose the carefully concealed truths : for feminine studies
Shakespeare was a woman, for african studies he was an Arab, the Cheikh
Zubayr !
Nevertheless, everything starts from a correct premise, to go beyond mere
apparences ; but, to do so, one imagines an other side of the mirror whose
delimitations are neat, precise, without the slightest ambiguity : the world
is seen as a rebus of which it suffices to find the key. In the transparent
world, everything is so immediate, legible, that one does no longer need to
ask questions, i.e., no longer need to think. This putting in question of the
very idea of question leads to the worse idiocies : if answers are so easy to
access, isitbecauseGodamusesHimselfwithpresentingusanencodedworld
1Due to the theme, I will exceptionnally be slightly ad hominem, but not too much.
1
ABfor the sole purpose of testing us ? Unless men are to blame, whose industry
is devoted to dissimulation for unawovable reasons ; such a behaviour thus
justifies the question , the cognitive protocol in fashion in Guantanamo.
One must anyway admit that a question need not have answers, that it is
not even bound to have some, since a great part of scientific activity consists,
precisely, in seeking the good questions. Thus, the correspondence between
planets and regular polyhedra, of which Kepler was so proud, is not even a
wrong hypothesis, it is an absurd connection, which only deserves a shrug
of the shoulders, a question that didn’t deserved to be posed, to be com-
pared to speculations linking the length of a ship with the age of its captain.
Transparency stumbles on the questioning as to the interest of questions,
next on the difficulty to find the answers to the supposedly good problems.
Indeed, answers are, mostly, partial : a half-answer accompanied with a new
question. The relation question/answer thus becomes an endless dialogue,
an explicitation process ; it is in this process, which yields no definitive and
totalising key, where the afterworld of apparences, i.e., knowledge, is to be
found.
1 Logics of transparency
There is in logic a fantasy of transparency that can be summarised by a
word : semantics. Before discussing the limitations of semantics, it is of
interest to discuss bad logic, the logic of those who do not have the words,
i.e., technical comptence : we only hear the music, i.e., this affirmation of
a transparent world. One should also quote the logical entries of Wikipedia,
usually written and rewritten by sectarians of transparency, but this material
is too labile.
1.1 Abduction
If A) B, it is because B needed A hence B) A . This amalgamation
between causes and effects trips over the wire ; in logic as well as in other
2domains, e.g., in politics : take this Devedjian explaining the misery of
suburbs by... the misdeeds of left wing politicians. As a sort of wink to
GiuseppeLongo,letusalsomentiontheabductivedimensionofthefantasyof
DNA(genetictransparency),witnessthe geneofpedophily deartoafriend
of the same Devedjian, Mr. Sarkozy. The unofficial model of abduction claim
is Sherlock Holmes, with his warped, undoubtedly amusing, deductions :
indeed, to analyse the ashes of a cigar and conclude that the criminal is 47,
2French politician, not quite a red .
2
BAAABBABback from India and limps from the left foot, is at least, unexpected. What
Sherlock Holmes actually supposes, is a world transparent at the level of
police, criminal activities, the key to this world being the science of ashes, a
3sortofnecromancy, positivebutjustasabsurd . Metaphorically, thispseudo-
science refers to this afterworld in which all questions are supposed to have
received their answer. There are however question which have no room in
this too polished (and policed) world, typically those of the form is this
problem well-posed ? .
The search for possible causes is, however, an ancient and legitimate ac-
tivity, albeitnotamodeofreasoning: thiswouldputapprencesincommand.
Mathematics created a special category for those possible causes, in want of
legitimation and, for that reason, in the limbs of reasoning : conjectures,
interesting hypotheses, on which one attracts attention. The process of in-
tegration of a conjecture in the corpus is complex and by no means transits
through an inversion of the sense of reasoning.
It should be observed that mathematical induction is close to abduc-
tion. Etymologically, induction is the reasoning by generalisation which, to
avoid being abusive, must transit through the emission of conjectures. What
one calls mathematical induction is an abduction which moves from possible
causestopossiblemethodsofconstructions, seeinfra thedevelopmentoncat-
egories. Mathematical induction is not, contrarily to abduction, a grotesque
mistake of reasoning ; it is nevertheless, see infra, a form of transparency.
1.2 Non monotonic logics
Still under the heading science for the half-wits , let us mention non
monotonic logics . They belong in our discussion because of the fantasy
of completeness, i.e., of the answer to all questions. Here, the slogan is what
is not provable is false : one thus seeks a completion by adding unprovable
statements. Every person with a minimum of logical culture knows that
this completion (that would yield transparency) is fundamentally impossi-
ble, because of the undecidability of the halting problem, in other terms, of
incompleteness, which has been rightly named : it denotes, not a want with
respect to a preexisiting totality, but the fundamentally incomplete nature
4of the cognitive process .
3On the other hand, the same Sherlock Holmes boasts ignoring the rotation of Earth
around the Sun : this is not part of positive science .
4To be put in relation with the unbounded operators of functional analysis, intrinsically
and desperately partial.
3
BAAABBAB1.3 Epistemic logic
The previous fiddlings attracted the cordial jealousy of epistemic logicians
who consider their domain as the worst logic ever, a claim that can be
grounded. Epistemic logic is an archipelago of rather afflictive abductive
anectodes, the most famous of which being that of the 49 Baghdad cuckolds.
5In this story, the Café du Commerce is admirative of the 48 iterations of the
same idiocy, anyway gone flat after the first step, and that we shall trans-
pose in Texas, between V (Vardi) and W (Bush) : they know that at least
one of them is wearing the horns, moreover V, knowing that W is betrayed,
cannot conclude ; but, since W does nor react either, V surmises that the
situation is symmetrical and, subsequently, slays his supposedly inconstant
spouse. This nonsense rests upon the idea of a perfect, immediate, transpar-
ent knowledge ; not too speak of the hidden assumption that the actors (at
least V) are familiar with epistemic logic .
Of course, as soon as this transparency faints, for instance if one takes
into account the intellectual limitations of W, one sees that V may have
killed an innocent wife. Technically speaking, the slowness of W corresponds
to the complexity of deduction, of algorithms and, in fine brings us back
to undecidability. This explains why epistemic logic never succeeded outside
thisCafé du Commerce where it flourishes : it contradicts the incompleteness
theorem.
Transparency takes here the form he who stays silent must have some-
thing to hide . These ways of forcing the mute into talking have a rear
6taste of torture : one thinks of the gégène de 1957, of the bathtub of
the Gestapo, a.k.a. waterboarding in Guantanamo and also of the 1937
7purges . Epistemic logic is thus the derisive scientific counterpart of totali-
tarism.
1.4 Explicit mathematics
Still within bad logic, but in the upper category, let us consider the explicit
mathematics of S. Feferman : it is a tentative bureaucratisation of science,
an attempt just as exciting as a fiction by Leonid Brezhnev. But, rather
than the mediocrity of the approach, we shall interrogate this extravagant
association mathematics + explicit : this is indeed an oxymoron.
5In France, the metaphoric location of commonplace ideas.
6Torture by electricity practiced by the French paratroopers.
7Yezhov’s ante litteram version of epistemic logic was organised along two types of